I'm really new to this, having only purchased my first orchid in May. I've looked into propagation by seed, and decided it wasn't worth it for me...I might try it later if I get hooked on growing orchids, but I haven't reached that point yet. Honestly, they're growing more tempting every day, but I like to think that I'm the one in charge - not my plants! :P So I have a couple questions: What is a meristem? And if you go by division, how do you know when the plant is ready to divide, and how do you divide it so as to cause the least damage to the original plant?

A meristem is tissue culture and is used to produce many copies of (usually) quality orchids. Not for the hobby grower as you need special equipment.

Do not be in a hurry to divide your plant as too small a division will take longer to recover and bloom.

What is the name of your Oncidium? A good sized divison might be the growing lead and four or five pseudobulbs behind that lead. Most growers pot on to a certain sized pot before dividing the plant and starting again in a smaller sized pot.

Another method of Onc. propogation - the sphag and bag method with back bulbs (dead leafless bulbs) - stuff them into a plastic bag with some damp sphagnum moss and let them be in a shelf away from light, after a few weeks new growth (roots and leaves and/or tiny bulb will sprout.)
But you should have atleast 3-4 viable healthy bulbs with leaves left on the main plant before you cut off a leafless back bulb for this operation.

Also, to divide you'll need a similar number of leafy bulbs in each divided section.

As noted above, if you've just bought this orchid you should let it adjust to your growing conditions for a few years before thinking of dividing, after a bloom cycle or two perhaps. It's using its energy adjusting to the new environment - you don t want to stress it further by cutting it in half.

Meristem is the microscopic point from where all plant growth occurs. Its a mass of totipotent (or pluripotent, I don't know developmental biology well) cells that are undifferentiated into specific functions. Everything about the plant comes from the meristem. On trees and shrubs, there is an axillary bud (meristem) at the base of every leaf with the potential to branch out.

Mericloning/meristem culture is where this growing point is removed from the plant and grown in sterile culture. After a small amount of time passes (a week?) this has grown considerably. It can be removed from sterile culture and cut up into smaller pieces. Those are then put back into sterile culture and allowed to grow again for a small amount of time. THESE are the cut again just as before. And on and on. Each of these little cut pieces has the potential to develop into a new plant.

Mericloning is a cheap way to to get massive amounts of plants. Each of these clones is identical to the original plant...for the most part. Tiny variations can still occur with this propagation method, but not by any significant degree. The thing about mericloning is that it destroys the original plant. This is why a lot of the time if you have a very valuable plant, people are more likely to propagate it by division rather than cloning.

That is not a correction. It is an enhancement. Might be a cheap way to get a massive amount of plants but it is interesting to note that mericlones are always more expensive here than orchids raised from seed.
You left out the bit about the shaking to stop the cells doing something or other and the dangers of mericloning mericlones. Best to always go back to the mother plant which hopefully has a couple of extra growing leads to survive destruction of one lead. But sometimes the mutations that occur in the mericloning process are beneficial. One example is the Yellow Mutation of Oncidium Sharry Baby 'Sweet fragrance' which might be the Oncidium owned by the OP.

LOL left them out cause I'm not familiar with them, other than possibly passing along viruses. Can you elaborate a bit? :)

That mericlones are more expensive I think makes a bit of sense, when you consider the labor required to actually divide the developing meristems, an additional step not seen in seed sown plants. Though my perception is, and correct me if I'm wrong, seed grown plants seem to generally be offered at younger stages than mericlones, which could also explain the price difference. Searching my memory, I'm not entirely sure I've seen a flask of mericlones available for sale. Not to say they aren't available, but seed sown flasks I think are more prevelant than mericlone flasks.

Here is a picture of a "good" mutation. Good as in round and filled in. You never hear much about the "bad" mutations.

Going back to the ever popular Sharry Baby 'Sweet Fragrance' Just say you are a newbie and buy one on the cheap from one of the bulk suppliers where they are sold mainly as a cheap bunch of flowers. You have to wonder how many mericlone steps back there are to the original plant. Each one of those steps increases the chance of mutation. If you look at the Sharry Babies on a show bench you will see lots of minor differences in the flowers.

Haven't a clue how many cells there in the typical meristem excision and how many cells there are in the divided pieces. Perhaps lots.

You mention the sterile conditions, but what about the chemicals used (if any) to make the cells divide faster. You can tell here that i really do not know what i'm talking about.